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Complete the Problem Set.

1.

A sample of 33 observations is selected from a normal population. The sample mean is 30, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H0 : ȝ ≤ 29

H1 : ȝ > 29

  • Is this a one- or two-tailed test?
  • What is the decision rule? (Round your answer to 3 decimal places.)
  • What is the value of the test statistic? (Round your answer to 2 decimal places.)
  • What is your decision regarding H0?
  • What is the p-value? (Round your answer to 4 decimal places.) p-value

“Two-tailed”-the alternate hypothesis is different from direction. “One-tailed”-the alternate hypothesis is greater than direction.

(Do not reject or reject) H0, when z >

Value of the test statistic

Do not reject

Reject

There is (sifficient or insifficient) evidence to conclude that the population mean is greater than 29.

2.

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $79 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.20. Over the first 41 days she was employed at the restaurant, the mean daily amount of her tips was $81.23. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $79?

  • State the null hypothesis and the alternate hypothesis.
  • State the decision rule.
  • Compute the value of the test statistic. (Round your answer to 2 decimal places.)
  • What is your decision regarding H0?
  • What is the p-value? (Round your answer to 4 decimal places.) p-value

H0: ȝ ≥ 79 ; H1: ȝ < 79

H0: ȝ ≤ 79 ; H1: ȝ > 79

H0: ȝ >79 ; H1: ȝ = 79

H0: ȝ = 79 ; H1: ȝ ≠ 79

Reject H0 if z < 1.65

Reject H1 if z < 1.65

Reject H0 if z > 1.65

Reject H1 if z > 1.65

Value of the test statistic

Do not reject H0 Reject H0

3.

The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 39 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 27 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 6.1 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 39?

H0 : ȝ ≤ 39

H1 : ȝ > 39

  • Compute the value of the test statistic. (Round your answer to 3 decimal places.)
  • What is your decision regarding H0?

Value of the test statistic

(Do not reject or reject) H0. The mean number of calls is (less or greater) than 39 per week.

4.

A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

  • State the null hypothesis and the alternate hypothesis.
  • State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
  • Compute the value of the test statistic. (Round your answer to 2 decimal places.)
  • Does this information disagree with the United Nations report? Apply the 0.01 significance level.

Reject H0 if t is not between

Value of the test statistic

(Reject or do not reject Ho). This data (Does not contradict or contradicts) the report.

5.

The following information is available.

H0 : ȝ > 220

H1 : ȝ < 220

A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.

  • Is this a one- or two-tailed test?
  • What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Reject or do not reject H0 when z <
  • What is the value of the test statistic? (Negative amount should be indicated by a minus sign.
  • What is your decision regarding H0?
  • What is the p-value? (Round your answer to 4 decimal places.) p-value

Two-tailed test

One-tailed test

Round your answer to 3 decimal places.)

Value of the test statistic

Reject

Do not reject

6.

Given the following hypotheses:

H0 : ȝ < 10

H1 : ȝ > 10

A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level:

  • State the decision rule. (Round your answer to 3 decimal places.)
  • Compute the value of the test statistic. (Round your answer to 3 decimal places.)
  • What is your decision regarding the null hypothesis?

Reject H0 if t >

Value of the test statistic

(Reject or do not reject) H0. There is (sufficient or insufficient) evidence to conclude that the population mean is greater than 10.

7.

Given the following hypotheses:

H0 : ȝ = 400

H1 : ȝ ≠ 400

A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:

  • State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
  • Compute the value of the test statistic. (Round your answer to 3 decimal places.)
  • What is your decision regarding the null hypothesis?

Reject H0 when the test statistic is (inside or outside) the interval ().

Value of the test statistic

Reject

Do not reject

 
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